Nodal analysis is a method of determining the voltage between nodes in an electrical circuit in terms of the branch currents.
Sample problem #2
Find I
The elements in this circuit are already converted to impedances.
First let’s identify the nodes in this circuit.
The node V2 has already its value which is 8 V because
of the supply connected under it.
Solving V1 could help identify the current entering the
–j3 ohm capacitor. From the node V1, we can get:
V1 (1/j6 + 1/-j3 + 1/8) – V2
(1/8) = 0
(The reciprocal of the
nearby impedances of node V1 times V1 minus the neighbor node of V1which is V2
times the reciprocal of the impedance that connects them.)
We could substitute V2= 8.
V1 (0.125+ j0.1666) – 8
(1/8) = 0
V1 (0.125 +0.1666) = 1
V1= 1/ (0.125+ j0.1666)
V1= 2.881 – j3.840 V
V1= 4.80 ∟-53.12V
To get I, just use ohms law and divide V1 to the capacitor.
Other problems that involves nodal and mesh analysis
requires matrix to solve for the unknown. The more complex the problem, the
greater the chance matrix is needed.
Supernode
Supernode
A super node is contains two nodes, one a non-reference
node and another node that may be a second non-reference node or the reference
node.
When a super node occurs in a circuit it involves
shortening the supply voltage and combining or adding the formulated equation
of the two nodes that are connected to the supply voltage. Then applying KVL to
the original circuit to get another equation and applying matrix, ohms law or
simple calculations to obtain the unknown value in the circuit.
